Bayesian nonparametric Plackett-Luce models for the analysis of preferences for college degree programmes

TL;DR

This paper introduces a Bayesian nonparametric extension of the Plackett-Luce model for clustering partial ranking data, specifically applied to preferences for college degree programs among Irish students, revealing meaningful clusters based on subject matter and location.

Contribution

It develops a novel Bayesian nonparametric model for infinite choice items and extends it with a Dirichlet process mixture, applied to real preference data.

Findings

Identified clusters of students with similar preferences.

Clusters characterized by subject matter and geographical location.

Model effectively handles infinite choice options.

Abstract

In this paper we propose a Bayesian nonparametric model for clustering partial ranking data. We start by developing a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice items. Our framework is based on the theory of random atomic measures, with the prior specified by a completely random measure. We characterise the posterior distribution given data, and derive a simple and effective Gibbs sampler for posterior simulation. We then develop a Dirichlet process mixture extension of our model and apply it to investigate the clustering of preferences for college degree programmes amongst Irish secondary school graduates. The existence of clusters of applicants who have similar preferences for degree programmes is established and we determine that subject matter and geographical location of the third level institution characterise these clusters.